The Dirichlet problem on almost Hermitian manifolds

DOI10.1007/s12220-020-00540-wzbMath1472.35131OpenAlexW3094429698MaRDI QIDQ2048305

Chang Li, Tao Zheng

Publication date: 5 August 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-020-00540-w

zbMATH Keywords

Dirichlet problema priori estimatealmost Hermitian manifoldMonge-Ampère-type equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05) Boundary value problems on manifolds (58J32)

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Gradient estimates for Monge-Ampère type equations on compact almost Hermitian manifolds with boundary ⋮ A subsolution theorem for the Monge-Ampère equation over an almost Hermitian manifold ⋮ On a class of fully nonlinear elliptic equations containing gradient terms on compact almost Hermitian manifolds ⋮ Unnamed Item ⋮ A gradient estimate for the Monge-Ampère equation on compact almost Hermitian manifolds ⋮ Second-order derivative estimates for a class of Hessian equations on compact almost Hermitian manifolds

Cites Work

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• Cohomological aspects in complex non-Kähler geometry
• Form-type equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
• \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry
• The Dirichlet problem for degenerate complex Monge-Ampère equations
• A gradient estimate in the Calabi-Yau theorem
• Immersed hypersurfaces with constant Weingarten curvature
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Closed Weingarten hypersurfaces in Riemannian manifolds
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• On the Dirichlet problem for Hessian equations
• Elliptic partial differential equations of second order
• The space of Kähler metrics.
• On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
• An almost complex Chern-Ricci flow
• Fully non-linear elliptic equations on compact Hermitian manifolds
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• Holomorphic discs and the complex Monge-Ampère equation.
• The Monge-Ampère equation for non-integrable almost complex structures
• Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
• Form-type Calabi-Yau equations
• Hermitian metrics, \((n-1,n-1)\) forms and Monge-Ampère equations
• The Dirichlet problem for a complex Monge-Ampère type equation on Hermitian manifolds
• Characteristic classes of Hermitian manifolds
• Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds
• Boundary Regularity for Viscosity Solutions of Fully Nonlinear Elliptic Equations
• The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold
• Monge–Ampère Equations on Complex Manifolds with Boundary
• Zur Abschätzung von Matrizennormen
• Taming symplectic forms and the Calabi-Yau equation
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices
• A variational theory of the Hessian equation
• Complex Monge Ampere Equations